To the 8 means that we can rewrite it as (9-25x^)^(1/8). This is important because 8 is even. Since we have an even number we can not have a -number under the radical. so the domain would be numebers such that 9-25x^2>=0.

So the domain is -3/5<=x<=3/5 or [-3/5,3/5]

A square root is an index of 1/2, so you've got...

( ( 9-25x^2 )^1/2 )^8.

When you've got 2 indices next to each other like that, you multiply them together, in this case giving...

( 9-25x^2 )^4.

The domain of this is all real numbers, since there isn't any number that can't be multiplied by itself 4 times!